Yes... as the name implies, leg rise is taken through the legs, which is caused by the straightening action of the knees (under the assumption that they are flexed to begin with).
Foot rise comes from the feet and ankles. The action occurs when one rises onto their toes (assuming that the feet are flat to begin with).
You may also hear of the concept of "body rise", which is, for all intents and purposes, synonymous with leg rise.
When the technique of a step calls for "No Foot Rise" or "Body Rise Only", it means that the rising action should only be taken through the straightening action of the knees, and not by rising up onto one's toes.
I hope this helps.
Sincerely, Jonathan Atkinson